The length of a rectangle is 8cm greater than its width. How do you find the dimensions of the rectangle if its area is 105cm²?

Question

14834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-01T03:13:09

Dimensions: $15$ $15$ cm $\times$ $xx$ $7$ $7$ cm

Let the length of the rectangle be $l$ $l$ and the width of the rectangle be $w$ $w$ ,

$l \cdot w = 105$ $l*w=105$

$l = w + 8$ $l=w+8$

Substitute $l = w + 8$ $l=w+8$ into $l \cdot w = 105$ $l*w=105$ ,

$(w + 8) \cdot w = 105$ $(w+8)*w=105$

Expand,

$w^{2} + 8 w - 105 = 0$ $w^2+8w-105=0$

Factor,

$(w - 7) (w + 15) = 0$ $(w-7)(w+15)=0$

Solve,

$w=7 or cancel(-15$ ( reject $-15$ as $w>0$ )

When $w=7$ ,

$l=7+8$
$l=15$

Hence, the length is $15$ cm and the width is $7$ cm.